University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 6 - Section 6.1 - Volumes Using Cross-Sections - Exercises - Page 356: 40

Answer

$$2 \pi$$

Work Step by Step

We need to integrate the integral to compute the volume. We have: $$Area =\pi (R^2- r^2)=\pi (4-4x)$$ Now, $$Volume = \pi \times \int_{0}^{1} (4-4x) dx \\ = \pi [4x-2x^2]_{0}^{1} \\= \pi (4-2-0+0) \\=2 \pi$$
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